In the framework of Einstein's general relativity all energy curves spacetime and hence exerts an attraction, but my question is whether it is an experimentally verified fact that energy that doesn't come from mass (such as photons) indeed attracts massive objects?

If you are willing to accept some version of Newton's 3rd law as a axiom I suppose that gravitational lensing is sufficient evidence, but the way the question is posed admits at least the possibility that the poster with not willing to simply stipulate this.
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dmckee♦May 21 '14 at 16:32

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This is an excellent question after the edit, I think.
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David Z♦May 21 '14 at 21:48

Strong laser beams do tend to attract nearby objects (particularly dust). But it has nothing to do with gravity. Electric field strength in beam is high enough to polarize nearby dust and it's electric attraction. For this reason I think it would be hard to measure curving spacetime with laser - you would need to somehow remove electric interaction from the picture and this just can't be done.
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Jarosław KomarMay 22 '14 at 13:21

The trouble is that spacetime is exceedingly hard to curve by any significant amount. Curving it is no problem if you have an astronomical body to hand, but measuring the curvature due to lab scale masses requires very fine measurements. Bearing in mind that mass is a very concentrated form of energy (by a factor of $c^2$) it's hard to see how we could ever get an intense enough source of light to create measurable curvature. There might be some indirect measurement possible, but none springs immediately to mind.

One way to think about it is that you would need as much light energy as in the rest mass of an astronomical body. Therefore, the only experiment I can think of that could work is to throw a small planet at a small anti planet.
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AronMay 22 '14 at 4:24

Yes, almost all of the mass-energy of ordinary matter is due to the gluonic field. Gluons are gauge bosons with zero mass (like photons). In the absence of gluons, the quarks making up protons and neutrons would have less than 2% of their usual mass. Since the measured gravitational interaction of matter includes the gluon-provided mass and is not just the quark-provided mass, we can be sure that gravitational interaction due to mass-energy does not discriminate between fundamentally massless and massive particles.

If you want to get back to photons, there is also a mass induced by the electromagnetic interaction. It makes protons a bit heavier than you would expect relative to neutrons. Again, there's every evidence that the gravitational interaction does not discriminate between mass induced by electromagnetism or any other source.

Of course, a beam of free photons is a bit different and requires more sophisticated calculation in relativity. Its very tiny gravitational interaction is impossible to measure using current technology.

"we can be sure that gravitational interaction due to mass-energy does not discriminate between fundamentally massless and massive particles" : chiral symmetry breaking gives mass to to nucleons even if gluons are massless, so I'm not sure it proves that massless energy curves spacetime
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agemOMay 22 '14 at 14:22

Chiral symmetry is broken by the gluonic field configuration of the vacuum, which produces chiral quark condensates as a secondary effect. In the absence of gluons, chiral symmetry would not be broken, whereas in the absence of sea quarks, it still is. One could use glueballs as a more direct example, except that accumulating enough glueballs to measure their gravitational effect would be impractical.
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XerxesMay 22 '14 at 21:04

The relationship between mass and curvature of spacetime is well-motivated, but not the consequence of some fundamental fact in GR.

There are plenty of experiments confirming the curvature of spacetime by masses, like gravitational lensing, the proper prediction of the perihelion of mercury, redshift in a gravitational field...

$E = mc^2$ is one of the most famous equations in physics, but also the single most one quoted out of context. The full equation reads

$$ E^2 = \vec p^2 c^2 + m^2 c^4$$

This implies that indeed, mass is just a form of energy and the other way round that there is no fundamental distinction (in GR) between objects with energy from rest mass or energy from momentum. This can be seen by the fact that photons DO interact with the gravitational field (see gravitational lensing), wile their rest mass $m = 0$.

There is indeed experimental evidence of curvature of spacetime by massive bodies, but is there experimental evidence of curvature of spacetime by massless bodies such as photons? Also how does the fact photons follow straight lines in curved spacetime (i.e. gravitational lensing) imply that they curve spacetime themselves?
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user44558May 21 '14 at 14:13

It doesn't imply that photon curve themselves spacetime, I don't know if there are direct experiment showing that photons curve spacetime, I just know it is implemented in cosmological model
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agemOMay 21 '14 at 15:02

@agemO There is the equivalence . When we see gravitational lensing the curvature is a synergy of the photons attracting the field and the field attracting the photons. In this sense you could ask is there an exeperiment showing that the falling apple attracts the earth as ~m1*m2/r**2
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anna vMay 21 '14 at 16:02

I am not sure to understand what you mean, in GR everything follows geodesic whatever its mass or energy, in your example if m2 is zero then there is no attraction. But indeed it can be hard to experimentally see a photon attracting a star
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agemOMay 21 '14 at 16:14

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Maybe you want to say that the fact photon follow geodesic theoretically imply they have to curve space time ? That we cannot say "let's say energy tensor only contain mass energy" without making GR inconsistent ?
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agemOMay 21 '14 at 16:19